RESISTANCE AND PRESSURE OF FLUIDS. 171 



a cubic foot of the fluid, R = the resistance of the fluid to 

 the motion of the body. Then, 



weight of the displaced fluid per second = avw. 

 But this mass has a velocity of v feet given to it; 

 /. work generated per second in displacing this fluid 



_ awv 3 



~W' 



But this work is performed by means of a force which 

 drags the body through the water at the rate of v feet per 

 second, against an equal and' opposite resistance R ; 



> 



that is, the resistance varies as the square of the ve- 

 locity. 



On account of eddies which are formed round the corners 

 of the body and in the rear, the value of R in (2) should be 

 multiplied by a constant k, giving 



t- 2 



R = kaw- (3) 



y 



HEM. The constant k is to be determined by experiment 

 for each form of solid. For a body whose transverse section 

 is circular, k does not differ much from unity ; for a flat 

 plate moving flat-wise, it is about 1.25. Resistances of this 

 kind, however, are very irregular, and may vary considera- 

 bly in the course of the same experiment. Different results 

 are therefore obtained by different experimentalists.* 



* See Rankine's Applied Mecha., p. 598 ; also CotterilTs Applied Mechs., p. 47*, 



